B-Spline Basis Functions

Abstract

Curves consisting of just one polynomial or rational segment are often inadequate. Their shortcomings are:

a high degree is required in order to satisfy a large number of constraints; e.g., (n − 1)-degree is needed to pass a polynomial Bézier curve through n data points. However, high degree curves are inefficient to process and are numerically unstable;

a high degree is required to accurately fit some complex shapes;

single-segment curves (surfaces) are not well-suited to interactive shape design; although Bézier curves can be shaped by means of their control points (and weights), the control is not sufficiently local.